Spectral gap for the cohomological Laplacian of ${\mathrm{SL}}_3(\mathbb{Z})$

Marek Kaluba, Piotr Mizerka, Piotr W. Nowak

We show that the cohomological Laplacian in degree 1 in the group cohomology of ${\mathrm{SL}}_3(\mathbb{Z})$ is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb…